In Fedora LiveUSB Creator, click Browse button in Use Existing Live CD frame and choose the .iso file you just downloaded

If you are planning to use Fedora Live USB only once to install Fedora permanently on the hard drive, continue to the next step.
If you want to boot from this USB regularly, it’s also a good idea to allocate some or all of the empty space on USB drive to Persistent Storage. Persistent Storage can be mounted as a drive in Fedora, while the rest of the USB drive will not be visible. This way you can keep documents and settings you need in Fedora on the same USB drive you are booting from.

Click Create Live USB. Wait for progress to reach 100% and for status to scream Complete! Close FedoraUSB Creator.

Step 2: Booting up from Fedora Live USB and installing Fedora on HDD

Insert USB stick into the system on which you want Fedora to be installed.

Boot up the system and make sure it boots from USB (on Thinkpad T60 for instance, you need to click ThinkVantage button while it boots, choose Boot from Temporary Device and then choose USB HDD from the menu).

When Fedora loads and reaches Login window, choose Automatic Login.

Once you are in, you should see Live System User at the right top corner. If you want to run Linux from USB every time, you are done. Otherwise, continue to the next step.

Click Install to Hard Drive icon on a desktop. Follow the wizard and proceed with further installation instructions.

Reboot, when done, and choose to boot from HDD this time (remove USB stick).